Simplify the expression. Write the answer using scientific notation. (9x10^2)(2x10^10)

Hello!

Answer:

[tex]\boxed{2y+11x}[/tex]

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

First, you switch sides. *Group like terms*

[tex]4y-2y+7x+4x[/tex]

Then, you add the similar to elements. You can also add the numbers from left to right.

[tex]4y-2y=2y[/tex]

[tex]2y+7x+4x[/tex]

[tex]7x+4x=11x[/tex]

[tex]\boxed{2y+11x}\checkmark[/tex], is the correct answer.

Hope this helps!

Have a nice day! :)

Answer:

2y + 11x

Step-by-step explanation:

Simplify the expression 4y+7x- 2y+4x​

To simplify any expression, combine the like terms by adding or subtracting

To simplify 4y+7x- 2y+4x​, combine the like terms

combine 4y and -2y, = 2y and

combine 7x and 4x = 11x

2y + 11x

Answer:

1.59

Step-by-step explanation:

log (2x-3)= log (3-x) -2

log (2x-3)/(3-x) =-2

If we remove log,

2x-3/(3-x) = e^-2

2x-3= 3e^-2 -xe^-2

2x+ xe^-2 = 3e^-2+3

x(2+e^-2) = 3( e^-2+1)

If you use calculator you will get answer nearly equal to 1.59.

Multiply last years rainfall by the percent of increase.

26 inches x 0.15 = 3.9 inches more.

Round the answer as needed.

First, we need to find 15% of last years total rainfall to estimate next years. To do this, multiply last years rain by the decimal form of 15%.

26*.15=3.9

There will be 3.9 more inches of rain predicted to fall next year.

Hope this helps!

Answer:

D) 8

Step-by-step explanation:

2^3 means 2 times itself 3 times:

2*2*2

2*2 is 4 so:

4*2

4*2 is 8 so the answer is D, 8!

D) 8

Mathematics written statement indicating the equality of 2 expressions. this consists of the sequence of symbols that are split in the left or right sides joined by the equal sign. example, 2 + 4 + 5 = 11 is an equation.

When equality holds, the total weight on the each side is the same. Equations often contain terms other than a unknowns. These other terms, which are assumed to known, is usually known as constants, coefficients and parameters

2^3 means 2 times itself 3 times:

2*2*2

2*2 is 4 so:

4*2

4*2 = 8

so the option is D, 8

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Answer:

The equation has infinity solutions

Step-by-step explanation:

3( x - 4 ) + 5 - x = 2 x - 7

⇒ Expand brackets

3 x - 12 + 5 - x = 2 x - 7

⇒ Simplify

2 x - 7 = 2 x - 7

Answer:

the first one is graph c and the second, graph b.

Step-by-step explanation:

They are both linear inequalities, so for both, you have to solve for x first. For the first one, since x is basically multiplied to 2 (2x), you have to divide both sides to get x by itself, and you get x>25. The graph has to have an opened circle, and the arrow should go to the right because all the numbers greater than 25 can be x. For the second one, you have to subtract 6 to both sides to get x by itself which then leaves you with ×<26. This one should also be an opened circle, and is going to the left, because all the numbers less than 26 can be x.

Answer:

first box c second box b

Step-by-step explanation:

ANSWER

b) The degree of the function is even so the ends of the graph continue in the same direction. because the leading coefficient is negative the left side of the graph continues down the coordinate plane and the right side also continues downward

EXPLANATION

The given polynomial function is

[tex]f(x) = - {x}^{4} + 1[/tex]

The degree of this function is even which is 4.

The function extends in the same direction at both ends.

In other words both ends continue in the same direction.

Since the coefficient of the leading term is negative, the graph extends to negative infinity at both ends.

The correct answer is B

Answer:

X int : 5

Y int : 15

Step-by-step explanation:

y=15

-

3x=15

3/3 15/3

x=5

Answer:

y-intercept=15 and x-intercept = 5

Step-by-step explanation:

We have the following equation:

3x + y = 15.

To find the x-intercept and y-intercept we have to do the following:

1. To find the y-intercept we need to make x=0, and solve for 'y' as follows:

3x + y = 15 ⇒ 3(0) + y = 15 ⇒ y=15

2. To find the x-intercept we need to make y=0, and solve for 'x' as follows:

3x + y = 15 ⇒ 3x + (0) = 15 ⇒ 3x = 15  ⇒ x=5

Therefore, the y-intercept=15 and x-intercept = 5

Answer:

Step-by-step explanation:

We know:

1. Diagonals of a rhombus are perpendicular.

2. Diagonals divide the rhombus on four congruent right triangles.

3. The sum of measures of acute angles in a right triangle is equal 90°.

Angles CAD and ACB are alternate angles. Therefore they are congruent:

m∠DAC = m∠ACB ⇒ m∠ACB = x°.

From 3. we have the equation:

(5x - 18) + x = 90

(5x + x) - 18 = 90              add 18 to both sides

6x = 108             divide both sides by 6

x = 18

Answer:

Option D

Step-by-step explanation:

In any Rhombus the diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.

So,

5x-18+x+90=180 ( Angles of a triangle add to 180 degrees)

Simplifying like terms:

6x+72=180

Subtracting  72 both sides :

6x= 108

Dividing by 6 both sides:

x=18.

Option D is correct.

Answer:

Im boutta fail my final

Step-by-step explanation:

1 like= 1 prayer

Answer:

D intersect E=D (the first one you have)

Step-by-step explanation:

D is a subset of E

That means all the elements in D are also in E

So the intersection of D and E is D.

The first thing you wrote is correct, that is, D intersect E=D is right

Answer:

[tex]D\cap E[/tex]=D

Step-by-step explanation:

We are given that D is not empty set but D is a subset of set E.

We have to find the true statement.

[tex]D\neq \phi[/tex]

D is  a subset of set E

Therefore,[tex]D\subset E\neq \phi[/tex]

Intersection: It is the set of common  elements of two sets.

Therefore,[tex]D\cap E[/tex]=D

Because E contains all elements of D .

Hence, Option A is true.

Answer:

[tex]x=15.56[/tex]

Step-by-step explanation:

We can use the law of sines here. However, we will first need to solve for the missing angle.

The interior angles of a triangle add up to 180.

Therefore,

[tex]35+90+x=180[/tex]

where [tex]x[/tex] is the missing angle.

[tex]35+90+x=180[/tex]

[tex]x+125=180[/tex]

[tex]x=55[/tex]

So the missing angle is 55 degrees.

Now we can use the law of sines to set up a proportion.

[tex]\frac{19}{sin(90)}=\frac{x}{sin(55)}[/tex]

Now simplify the equation.

[tex]x=15.56[/tex]

Rounded to the nearest hundredth.

Answer:

x ≈ 19.6

Step-by-step explanation:

Since the triangle is right use the cosine ratio to solve for x

cos35° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{19}[/tex]

Multiply both sides by 19

19 × cos35° = x, hence

x ≈ 19.6 ( to 1 dec. place )

Answer:

14.08 m

Step-by-step explanation:

Start by finding the area of the fence and the area of the garden. Garden- 10.1*4.2=42.42   Fence-11.3*5=56.5

Now subtract the two values. 56.5-42.42=14.08

Divide 45 by 3 ( the quantity of consecutive numbers) This will give you the middle number, then use the number higher and lower.

45/3 = 15

14 + 15 + 16 = 45

The 3 numbers are 14, 15 and 16

Answer:

p^4 p^3 P^2

Step-by-step explanation:

Look at the numbers and put them in order from largest to smallest number.

Answer:Answer:

p^4 p^3 P^2

Step-by-step explanation:

Look at the numbers and put them in order from largest to smallest number.

Answer:

Height of parallelogram = 5.07 inches

Step-by-step explanation:

We are given Area of Parallelogram = 32 in^2

Height of Parallelogram = ?

Base of Parallelogram = 6.3 in

The formula to find the Area of Parallelogram is:

Area of Parallelogram = Base * Height

32 = 6.3 * Height

=> Height = 32/6.3

=> Height = 5.07 inches

So, height of parallelogram = 5.07 inches

The missing variable for this parallelogram is the height, which is 5.08 inches.

We begin with the formula for the area of a parallelogram:

We plug in all given information.  We know the area, 32 in², and we know the base, 6.3 in:

Next we solve for our variable, h.  Since 6.3 and h are beside each other, we know they have been multiplied.  To cancel this, we will divide both sides by 6.3:

This means that the missing variable, the height, is approximately 5.08 inches.

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Keywords: missing variables, missing measurements, area of parallelogram, missing side of parallelogram

Answer:

Simplify by combining like terms, she combined 1/2 and 1 which equals 3/2. Your answer is A.

Step-by-step explanation:

The missing step in Fiona's solution to the equation 1/2 - 1/3(6x - 3) = -13/2 was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2.

To find the missing step of Fiona's solution, we first need to simplify the equation. The given equation is 1/2 - 1/3(6x - 3) = -13/2. The missing step may be the distribution of the 1/3 onto the (6x - 3). This leads to 1/2 - (2x - 1) = -13/2.

Following this, we need to remove the fraction on the left side of the equation by multiplying the entire equation by 2. This gives 1 - (4x - 2) = -13. Finally, simplifying this further gives us -4x = -16, and solving for x we get x = 4.

Therefore, Fiona's missing step was the distribution of the 1/3 to each term in the parentheses and the multiplication of the equation by 2 to get rid of fractions.

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Answer:

104

Step-by-step explanation:

< MON  = 180 - 104 = 76

This is an isosceles triangle.

There fore < OMN = 76

< LMN =  180 -76 = 104

[tex]n[/tex] - 4-digit number

[tex]q[/tex] - quotient

[tex]131q+112=n\\132q+98=n\\\\131q+112=132q+98\\q=14\\\\131\cdot14+112=n\\\boxed{n=1946}[/tex]

The four-digit number which has the remainder of 112 when divided by 131 is 1946.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, number which has the remainder of 112 when divided by 131.

Let n be the number and q be the quotient.

We know that, Dividend = Divisor × Quotient + Remainder

Now, n=131×q+112 ------(i)

The remainder of 98 when divided by 132.

That is, n=132×q+98 ------(ii)

From equation (i) and (ii), we get

131×q+112=132×q+98

131q+112=132q+98

132q-131q=112-98

q=14

Substitute q=14 in equation (i), we get

n=131×14+112

n=1946

Therefore, the four digit number is 1946.

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Answer:

Step-by-step explanation:

Perimeter= 2L+2W. If L=3W(three times the width) then 2(3W)+2W=112. Or 6W+2W=112 which is equal to 8W=112. To solve for the width, divide both sides by 8 and find 112/8=14, therefore W=14.

Answer:

14 cm

Step-by-step explanation:

Given the length is 3 times the width

If each width is denoted by W, then each length is L = 3W

Perimeter (add up all lengths and widths),

= L + L + W + W

= 3W + 3W + W + W

= 8W

Given that the max perimeter is 112cm

hence 8W = 112,

W = 14 cm at most

Answer:

$ 2.737

Step-by-step explanation:

The amount of tax is 6% of the purchase price

Solution

[tex]\frac{6}{100} *45.62=2.7372[/tex]

Amount of tax will be $2.737

The amount of tax is 6% of the purchase price

Solution

\frac{6}{100} *45.62=2.7372

Amount of tax will be $2.737

Answer:

yes

Step-by-step explanation:

You can perform the "line test." If it is a function, there will not be two x's of the same value. In this case, x is 2,6,-1. No number repeats, thus making a function.

Answer:

Function:

(7, -4) (0, 9), (2, -2)

(-6, 5), (-5,6), (8,2)

(2, 3), (6, -5), (-1,3)

Not a Function:

(1, 9), (-3, -2), (1, -4)

(0, 3), (0, 7), (4, 0)

Step-by-step explanation:

I got it right on edge lol

also none of the other answers for this question on here are right

First you are going to multiply the number by the percent. 9,895 x 20= 197,900.

Now divide the answer by 100. 197,900 / 100= 1,979.

This means the car salesman should make 1,979 from the car sale.

Remember, multiply the number by the percent, then divide that answer by 100.

I hope this helps! :)

Answer:

k(x) = (3g + 5h)(x) ⇒ (1)

k(x) = (5h - 3g)(x) ⇒ (3)

k(x) = (h - g)(x) ⇒ (2)

k(x) = (g + h)(x) ⇒ (4)

k(x) = (5g + 3h)(x) ⇒ (5)

k(x) = (3h - 5g)(x) ⇒ (6)

Step-by-step explanation:

* To solve this problem we will substitute h(x) and g(x) in k(x) in the

  right column to find the corresponding function formula in the

  left column

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

- Lets start with the right column

# k(x) = (3g + 5h)(x)

∵ g(x) = -3^x + 5

∵ 3g(x) = 3[-3^x + 5] = [3 × -3^x + 3 × 5]

- Lets simplify 3 × -3^x

 take the negative out -(3 × 3^x), and use the rule a^n × a^m = a^(n+m)

∴ -3(3 × 3^x) = -(3^x+1)

∴ 3g(x) = -3^x+1 + 15

∵ h(x) = 5 - 3x

∵ 5h(x) = 5[5 - 3x] = [5 × 5 - 5 × 3x] = 25 - 15x

- Now substitute 3g(x) and 5h(x) in k(x)

∵ k(x) = (3g + 5h)(x)

∴ k(x) = -3^x+1 + 15 + 25 - 15x ⇒ simplify

∴ k(x) = 40 - 3^x+1 - 15x

∴ k(x) = 40 - 3^x+1 - 15x ⇒ k(x) = (3g + 5h)(x)

* k(x) = (3g + 5h)(x) ⇒ (1)

# k(x) = (5h - 3g)(x)

∵ 5h(x) = 25 - 15x

∵ 3g(x) = -3^x+1 + 15

∵ k(x) = (5h - 3g)(x)

∴ k(x) = 25 - 15x - (-3^x+1 + 15) = 25 -15x + 3^x+1 - 15 ⇒ simplify

∴ k(x) = 10 + 3^x+1 - 15x

∴ k(x) = 10 + 3^x+1 - 15x ⇒ k(x) = (5h - 3g)(x)

* k(x) = (5h - 3g)(x) ⇒ (3)

# k(x) = (h - g)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (h - g)(x)

∴ k(x) = 5 - 3x - (-3^x + 5) = 5 - 3x + 3^x - 5 ⇒ simplify

∴ k(x) = 3^x - 3x

∴ k(x)= 3^x - 3x ⇒ k(x) = (h - g)(x)

* k(x) = (h - g)(x) ⇒ (2)

# k(x) = (g + h)(x)

∵ h(x) = 5 - 3x

∵ g(x) = -3^x + 5

∵ k(x) = (g + h)(x)

∴ k(x) = -3^x + 5 + 5 - 3x ⇒ simplify

∴ k(x) = 10 - 3^x - 3x

∴ k(x)= 10 - 3^x - 3x ⇒ k(x) = (g + h)(x)

* k(x) = (g + h)(x) ⇒ (4)

# k(x) = (5g + 3h)(x)

∵ g(x) = -3^x + 5

∵ 5g(x) = 5[-3^x + 5] = [5 × -3^x + 5 × 5] = 5(-3^x) + 25

∴ 5g(x) = -5(3^x) + 25

∵ h(x) = 5 - 3x

∵ 3h(x) = 3[5 - 3x] = [3 × 5 - 3 × 3x] = 15 - 9x

- Now substitute 5g(x) and 3h(x) in k(x)

∵ k(x) = (5g + 3h)(x)

∴ k(x) = -5(3^x) + 25 + 15 - 9x ⇒ simplify

∴ k(x) = 40 - 5(3^x) - 9x

∴ k(x) = 40 - 5(3^x) - 9x ⇒ k(x) = (5g + 3h)(x)

* k(x) = (5g + 3h)(x) ⇒ (5)

# k(x) = (3h - 5g)(x)

∵ 3h(x) = 15 - 9x

∵ 5g(x) = -5(3^x) + 25

∵ k(x) = (3h - 5g)(x)

∴ k(x) = 15 - 9x - [-5(3^x) + 25] = 15 - 9x + 5(3^x) - 25 ⇒ simplify

∴ k(x) = 5(3^x) - 9x - 10

∴ k(x) = 5(3^x) - 9x - 10 ⇒ k(x) = (3h - 5g)(x)

* k(x) = (3h - 5g)(x) ⇒ (6)

Answer:

(-7,3)

Step-by-step explanation:

Given that point (-7,1) is on the graph of f(x), means that

[tex]f(-7)=1[/tex]

To find the corresponding point for the function y=3f(x), you have to find the value of the function at x=-7.

Substitute x=-7 into the function's expression:

[tex]y=3f(-7)[/tex]

Since f(-7)=1, we have that

[tex]y=3\cdot 1=3[/tex]

Hence, the corresponding point has coordinates (-7,3)

To find the corresponding point for the function 3f(x), multiply the y-coordinate of the given point by 3.

To find the corresponding point for the function 3f(x), we need to multiply the y-coordinate of the given point by 3.

Given that (-7,1) is on the graph of f(x), we multiply the y-coordinate by 3 to get (1*3) = 3.

Therefore, the corresponding point for the function 3f(x) is (-7,3).

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Answer:

x=2

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

B. [tex]y-9=2(x-1)[/tex]

Step-by-step explanation:

We have been given graph of a line on coordinate plane. We are asked to find the equation of our given line.

First of all, we will find slope of our line using points [tex](-2,3)\text{ and }(1,9)[/tex] in slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{9-3}{1-(-2)}[/tex]

[tex]m=\frac{6}{1+2}[/tex]

[tex]m=\frac{6}{3}[/tex]

[tex]m=2[/tex]

We can see that our given equations are in point-slope form of equation: [tex](y-y_1)=m(x-x_1)[/tex], where,

m = Slope,

[tex](x_1,y_1)[/tex] = Coordinates of point on line.

We can get two equations of our line in point-slope form as:

[tex](y-3)=2(x--2)[/tex]

[tex](y-3)=2(x+2)[/tex] or

[tex](y-9)=2(x-1)[/tex]

Upon looking at our given choices, we can see that option B is the correct choice.

Answer:

b d e f

Step-by-step explanation: